Aberrismic theory: Difference between revisions
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Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps | Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps | ||
<math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here <math>T</math> is a temperament map defined on the 2.p<sub>1</sub>....p<sub>s</sub> subgroup), determined by differing choices of <math>\alpha(\mathbf{L}), \alpha(\mathbf{m}), \alpha(\mathbf{s})</math> and subject to the constraint that <math>5\alpha(\mathbf{L}) + 2\alpha(\mathbf{m}) + 3\alpha(\mathbf{s}) = T(2).</math> | <math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here <math>T</math> is a temperament map defined on the 2.p<sub>1</sub>....p<sub>s</sub> subgroup), determined by differing choices of <math>\alpha(\mathbf{L}), \alpha(\mathbf{m}), \alpha(\mathbf{s})</math> and subject to the constraint that <math>5\alpha(\mathbf{L}) + 2\alpha(\mathbf{m}) + 3\alpha(\mathbf{s}) = T(2).</math> <!--Technically, there are two "degrees of freedom", namely the choice of temperament and the choice of where to map the scale steps. The assignments of scale steps to tempered intervals is chosen to maximize coverage of important LCJI intervals.--> | ||
== Code == | == Code == | ||